Abstract
We propose a new kind of moment invariants with respect to an affine transformation. The new invariants are constructed in two steps. First, the affine transformation is decomposed into scaling, stretching and two rotations. The image is partially normalized up to the second rotation, and then rotation invariants from Gaussian-Hermite moments are applied. Comparing to the existing approaches – traditional direct affine invariants and complete image normalization – the proposed method is more numerically stable. The stability is achieved thanks to the use of orthogonal Gaussian-Hermite moments and also due to the partial normalization, which is more robust to small changes of the object than the complete normalization. Both effects are documented in the paper by experiments. Better stability opens the possibility of calculating affine invariants of higher orders with better discrimination power. This might be useful namely when different classes contain similar objects and cannot be separated by low-order invariants.
This work has been supported by the Czech Science Foundation (Grant No. GA18-07247S) and by the Praemium Academiae, awarded by the Czech Academy of Sciences. Bo Yang has been supported by the Fundamental Research Funds for the Central Universities (No. 3102018ZY025) and the Fund Program for the Scientific Activities of the Selected Returned Overseas Professionals in Shaanxi Province (No. 2018024).
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Notes
- 1.
The reader may recall the so-called “indirect approach” to constructing rotation invariants from Legendre [5, 15] and Krawtchouk [37] moments. The authors basically expressed geometric moments in terms of the respective OG moments and substituted into (9). They ended up with clumsy formulas of questionable numerical properties.
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Flusser, J., Suk, T., Yang, B. (2019). Orthogonal Affine Invariants from Gaussian-Hermite Moments. In: Vento, M., Percannella, G. (eds) Computer Analysis of Images and Patterns. CAIP 2019. Lecture Notes in Computer Science(), vol 11679. Springer, Cham. https://doi.org/10.1007/978-3-030-29891-3_36
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